Industry: Mining and Natural Resources Product: ModelRisk Application: Quantifying geological and financial uncertainty in mineral exploration
Run a copper-gold exploration prospect 80,000 times and the median outcome is a $22M loss — the sunk cost of geophysics and drilling on a hole that finds nothing. The mean outcome is a $26M gain. Both numbers describe the same prospect, and the gap between them is the entire problem with valuing exploration on a point estimate: the project almost never lands anywhere near its average. Only 3% of trials end in the black, but those few carry a tail that runs out past $1.6 billion at the 99th percentile. A multinational explorer used Vose Software's ModelRisk to put exactly this distribution in front of its investment committee — and to show that a prospect with a 97% chance of losing money was still, in expectation, worth drilling.
A deterministic model takes a "most likely" grade, a "most likely" tonnage, a "most likely" metal price, multiplies them, and reports a single NPV. For a producing mine that is defensible. For an exploration prospect it is meaningless, because the outcome is not a value — it is a bimodal lottery: a thin spike of near-certain small losses (the dry holes) and a long, thin upper tail (the rare company-making discovery). The mean of that lottery, $26M, sits in a region of the NPV axis the project will essentially never occupy. No single number can represent it; only the distribution can.
The chart above makes the shape literal. On a log-frequency axis, the spike of failed prospects towers at the -$22M sunk-cost mark while the discovery tail decays slowly across the entire positive axis. This is the canonical fat-tailed, right-skewed profile of frontier exploration — and it is precisely the shape a single-point feasibility number erases.
Before there is any deposit to value, the prospect must clear three sequential technical gates. The model treats each as a Bernoulli trial calibrated to the company's regional hit-rate database:
Multiplied through, the unconditional probability of a discovery is 7.7% — and a miss at any gate ends the project at the cumulative exploration spend already incurred ($22M: $3M geophysics, $9M first-pass drilling, $10M appraisal).
For the prospects that do survive, the resource is built bottom-up. Total ore volume is V = A × T × D — mineralised area A (Triangular), thickness T (LogNormal, right-skewed), and ore density D (Normal). Contained metal is M = V × G, where copper-equivalent grade G follows a Beta distribution (mean 0.9%) bounded on a realistic interval. The simulated discovered deposit averages 0.79 Mt of contained Cu-eq (P50 = 0.62 Mt, P90 = 1.54 Mt) — a wide spread that reflects how little is known from early drill spacing.
V = A × T × D
A
T
D
M = V × G
G
A discovered tonne of metal is not a banked dollar. The model layers four further uncertain drivers onto each discovery:
R
The result is sobering even conditional on having found something: the discovered-deposit NPV averages $80M but has a P10 of -$1,382M and a P90 of +$1,988M, and 60% of discoveries are sub-economic — they get shelved, not built. Finding a deposit is necessary, not sufficient.
The power of the simulation is that it can re-cut the NPV distribution conditional on surviving to each stage gate — which is exactly the information a stage-gate investment decision needs.
At grassroots, the prospect's risked NPV has a mean of $64M but a P90 still in the red at -$22M — nine times in ten you are looking at the sunk cost. Clear the geophysics gate and the mean rises to $195M with a P90 of $426M. Land a first-drill intersection and the curve transforms: mean $595M, P90 $2,005M. Each gate does not change the geology — it changes what you know, compressing the loss mass and fattening the upper tail. That repricing is the literal value of information, and it is invisible to any deterministic model.
Ranking the drivers of a discovered deposit's NPV, Cu-eq grade dominates with a ±$1,605M swing, followed closely by metal price (±$1,536M) and deposit tonnage/thickness (±$1,455M). Capex (±$1,056M) and operating cost (±$980M) follow, with metallurgical recovery (±$175M) the least influential. The ranking drove the budget: because grade and tonnage are the two largest and the two most reducible through drilling, the company funded an additional infill-drilling program rather than spending the same dollars on early metallurgical test-work — recovery simply was not where the uncertainty lived.
Committing the full $22M program produces three terminal outcomes: a 3.0% chance of an economic discovery worth +$1,492M net of spend, a 4.7% chance of a discovery that proves sub-economic and is shelved at the -$22M sunk cost, and a 92.3% chance of no discovery at all. Probability-weighted, the drilling decision is worth +$24M against the $0 of walking away. The expected value is positive — but it is entirely carried by the 3% branch. This is the decision a point estimate cannot frame honestly: a 97%-chance-of-loss prospect that is still, in cold expectation, the right one to drill, provided the company has the balance-sheet and the portfolio to absorb the near-certain individual loss in pursuit of the rare outsized win.
A producing mine can be valued with a number. An exploration prospect cannot — its honest valuation is a distribution in which the most likely outcome is a loss and the expected outcome is a profit, and the only tool that holds both truths at once is Monte Carlo simulation.